Math Problem Statement

f h(x) is the inverse of f(x), what is the value of h(f(x))

Solution

If h(x)h(x) is the inverse of f(x)f(x), then by the definition of inverse functions, applying hh to f(x)f(x) returns the original input xx. In mathematical terms, this can be written as:

h(f(x))=xh(f(x)) = x

This is because the function f(x)f(x) maps xx to some value, and the inverse function h(x)h(x) undoes that mapping, bringing it back to xx.

Would you like more details on inverse functions, or do you have any questions?

Here are 5 related questions to expand on this:

  1. What is the formal definition of an inverse function?
  2. How do you find the inverse of a function algebraically?
  3. What is the graphical relationship between a function and its inverse?
  4. Can all functions have inverses? Why or why not?
  5. What happens if f(x)f(x) is not one-to-one? Can it still have an inverse?

Tip: A function must be one-to-one (injective) in order to have an inverse function.

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Function Composition

Formulas

h(f(x)) = x, where h(x) is the inverse of f(x)

Theorems

Inverse Function Theorem

Suitable Grade Level

Grades 9-12